What is the significance of Captain Beatty's quotes towards Montag in Fahrenheit 451?

Captain Beatty is a very clever man. He knows long before Montag knows himself that he will slide down the slippery slope to reading books. Captain Beatty knows because he was there once himself. So in a condescending way, Beatty drops little hints throughout the book that show he knows Montag has a stash of books, stole a book from the old woman's house, and has become engrossed in reading.

First, Beatty goes over to...

Captain Beatty is a very clever man. He knows long before Montag knows himself that he will slide down the slippery slope to reading books. Captain Beatty knows because he was there once himself. So in a condescending way, Beatty drops little hints throughout the book that show he knows Montag has a stash of books, stole a book from the old woman's house, and has become engrossed in reading.

First, Beatty goes over to Montag's house after the night the woman burns herself up with her books. Montag has taken a sick day to deal with how unfathomable the event was. Beatty even seems to care at this point because he tells Montag the whole history of how books declined in value and popularity, and then why their society outlawed them. At the end of his lecture, Beatty says the following:

"One last thing. . . At least once in his career, every fireman gets an itch. What do the books say, he wonders. Oh, to scratch that itch, eh? . . . if a fireman accidentally, really not intending anything, takes a book home with him. . . We let the fireman keep the book twenty-four hours. If he hasn't burned it by then, we simply come burn it for him" (62).

What Montag doesn't know is that Beatty already knows he has books because he's been slipping Montag's scent to the Mechanical Hound. Montag later hears the Hound outside his house a couple of times and doesn't think twice about it.

Near the end of the story, Montag returns to the firehouse and Beatty says he has had a dream where the two of them are quoting passages of books in a debate about whether books are useful or not. Beatty verbally fires quote after quote at Montag to confuse him and to show him who's the better man. Montag has his friend Faber in his ear on what they call the green bullet, and he tries to calm him down by saying, "Montag, hold on! . . . He's muddying the waters!" (107). It's a war of words. Beatty is trying to show Montag that all the words in the world, if used all at once, can cause confusion, frustration and unhappiness. That's the whole reason they burn books—so people can live without such confusion.

Fortunately, Montag doesn't submit to Beatty's games; and even though Montag is eventually reported by his wife and forced to burn his own house down, he gets revenge and burns Beatty, too.